Reducing the influence of geometry-induced gradient deformation in liquid chromatographic retention modelling

Enhancing LC×LC separations through multi-task Bayesian optimization

Method development in comprehensive two-dimensional liquid chromatography (LC×LC) is a challenging process. The interdependencies between the two dimensions and the possibility of incorporating complex gradient profiles, such as multi-segmented gradients or shifting gradients, make trial-and-error method development time-consuming and highly dependent on user experience. Retention modeling and Bayesian optimization (BO) have been proposed as solutions to mitigate these issues. However, both approaches have their strengths and weaknesses. On the one hand, retention modeling, which approximates true retention behavior, depends on effective peak tracking and accurate retention time and width predictions, which are increasingly challenging for complex samples and advanced gradient assemblies. On the other hand, Bayesian optimization may require many experiments when dealing with many adjustable parameters, as in LC×LC. Therefore, in this work, we investigate the use of multi-task Bayesian optimization (MTBO), a method that can combine information from both retention modeling and experimental measurements. The algorithm was first tested and compared with BO using a synthetic retention modeling test case, where it was shown that MTBO finds better optima with fewer method-development iterations than conventional BO. Next, the algorithm was tested on the optimization of a method for a pesticide sample and we found that the algorithm was able to improve upon the initial scanning experiments. Multi-task Bayesian optimization is a promising technique in situations where modeling retention is challenging, and the high number of adjustable parameters and/or limited optimization budget makes traditional Bayesian optimization impractical.

Computer-driven optimization of complex gradients in comprehensive two-dimensional liquid chromatography

Method development in comprehensive two-dimensional liquid chromatography (LC × LC) is a complicated endeavor. The dependency between the two dimensions and the possibility of incorporating complex gradient profiles, such as multi-segmented gradients or shifting gradients, renders method development by "trial-and-error" time-consuming and highly dependent on user experience. In this work, an open-source algorithm for the automated and interpretive method development of complex gradients in LC × LC-mass spectrometry (MS) was developed. A workflow was designed to operate within a closed-loop that allowed direct interaction between the LC × LC-MS system and a data-processing computer which ran in an unsupervised and automated fashion. Obtaining accurate retention models in LC × LC is difficult due to the challenges associated with the exact determination of retention times, curve fitting because of the use of gradient elution, and gradient deformation. Thus, retention models were compared in terms of repeatability of determination. Additionally, the design of shifting gradients in the second dimension and the prediction of peak widths were investigated. The algorithm was tested on separations of a tryptic digest of a monoclonal antibody using an objective function that included the sum of resolutions and analysis time as quality descriptors. The algorithm was able to improve the separation relative to a generic starting method using these complex gradient profiles after only four method-development iterations (i.e., sets of chromatographic conditions). Further iterations improved retention time and peak width predictions and thus the accuracy in the separations predicted by the algorithm.

Capacitively coupled contactless conductivity detection to account for system-induced gradient deformation in liquid chromatography

The time required for method development in gradient-elution liquid chromatography (LC) may be reduced by using an empirical modelling approach to describe and predict analyte retention and peak width. However, prediction accuracy is impaired by system-induced gradient deformation, which can be especially prominent for steep gradients. As the deformation is unique to each LC instrument, it needs to be corrected for if retention modelling for optimization and method transfer is to become generally applicable. Such a correction requires knowledge of the actual gradient profile. The latter has been measured using capacitively coupled "contactless" conductivity detection (C⁴D), featuring a low detection volume (approximately 0.05 μL) and compatibility with very high pressures (80 MPa or more). Several different solvent gradients, from water to acetonitrile, water to methanol, and acetonitrile to tetrahydrofuran, could be measured directly without the addition of a tracer component to the mobile phase, exemplifying the universal nature of the approach. Gradient profiles were found to be unique for each solvent combination, flowrate, and gradient duration. The profiles could be described by convoluting the programmed gradient with a weighted sum of two distribution functions. Knowledge of the exact profiles was used to improve the inter-system transferability of retention models for toluene, anthracene, phenol, emodin, sudan-I and several polystyrene standards.

The use of predictive models to develop chromatography-based purification processes

Chromatography is the workhorse of biopharmaceutical downstream processing because it can selectively enrich a target product while removing impurities from complex feed streams. This is achieved by exploiting differences in molecular properties, such as size, charge and hydrophobicity (alone or in different combinations). Accordingly, many parameters must be tested during process development in order to maximize product purity and recovery, including resin and ligand types, conductivity, pH, gradient profiles, and the sequence of separation operations. The number of possible experimental conditions quickly becomes unmanageable. Although the range of suitable conditions can be narrowed based on experience, the time and cost of the work remain high even when using high-throughput laboratory automation. In contrast, chromatography modeling using inexpensive, parallelized computer hardware can provide expert knowledge, predicting conditions that achieve high purity and efficient recovery. The prediction of suitable conditions in silico reduces the number of empirical tests required and provides in-depth process understanding, which is recommended by regulatory authorities. In this article, we discuss the benefits and specific challenges of chromatography modeling. We describe the experimental characterization of chromatography devices and settings prior to modeling, such as the determination of column porosity. We also consider the challenges that must be overcome when models are set up and calibrated, including the cross-validation and verification of data-driven and hybrid (combined data-driven and mechanistic) models. This review will therefore support researchers intending to establish a chromatography modeling workflow in their laboratory.

An approach to high throughput measurement of accurate retention data in liquid chromatography

Efforts to model and simulate various aspects of liquid chromatography (LC) separations (e.g., retention, selectivity, peak capacity, injection breakthrough) depend on experimental retention measurements to use as the basis for the models and simulations. Often these modeling and simulation efforts are limited by datasets that are too small because of the cost (time and money) associated with making the measurements. Other groups have demonstrated improvements in throughput of LC separations by focusing on "overhead" associated with the instrument itself - for example, between-analysis software processing time, and autosampler motions. In this paper we explore the possibility of using columns with small volumes (i.e., 5 mm x 2.1 mm i.d.) compared to conventional columns (e.g., 100 mm x 2.1 mm i.d.) that are typically used for retention measurements. We find that isocratic retention factors calculated for columns with these dimensions are different by about 20%; we attribute this difference - which we interpret as an error in measurements based on data from the 5 mm column - to extra-column volume associated with inlet and outlet frits. Since retention factor is a thermodynamic property of the mobile/stationary phase system under study, it should be independent of the dimensions of the column that is used for the measurement. We propose using ratios of retention factors (i.e., selectivities) to translate retention measurements between columns of different dimensions, so that measurements made using small columns can be used to make predictions for separations that involve conventional columns. We find that this approach reduces the difference in retention factors (5 mm compared to 100 mm columns) from an average of 18% to an average absolute difference of 1.7% (all errors less than 8%). This approach will significantly increase the rate at which high quality retention data can be collected to thousands of measurements per instrument per day, which in turn will likely have a profound impact on the quality of models and simulations that can be developed for many aspects of LC separations.

Perspectives on the Use of Retention Modeling to Streamline 2D-LC Method Development: Current State and Future Prospects

The history of multidimensional liquid chromatography (MDLC) has been dominated by methods that have been developed using highly empirical, experience-driven, trial-and-error approaches. These approaches have been sufficient in progressing the field forward scientifically, primarily in academic research laboratories. However, more widespread usage of multidimensional separations will require more systematic approaches to method development that rely less on user experience and lower the barriers to development and use of methods by a wider community of users. In this mini-review, we discuss recent research aimed at developing such systematic, model-driven approaches to streamline method development and speculate about likely advances in the same direction in the near future. It seems likely that such model-driven approaches would be particularly helpful for methods developed for analyzing biopharmaceutical molecules, which tend to be very sensitive to slight changes in method conditions (for example, mobile phase composition).

Accuracy of retention model parameters obtained from retention data in liquid chromatography

In liquid chromatography (LC), it is often very useful to have an accurate model of the retention factor, k, over a wide range of isocratic elution conditions. In principle, the parameters of a retention model can be obtained by fitting either isocratic or gradient retention factor data. However, in spite of many of our own attempts to accurately predict isocratic k values using retention models trained with gradient retention data, this has not worked in our hands. In the present study we have used synthetic isocratic and gradient retention data for small molecules under reversed-phase LC conditions. This allows us to discover challenges associated with predicting isocratic k's without the confounding influences of experimental issues that are difficult to model or eliminate. The results indicate that it is not currently possible to consistently predict isocratic retention factors for small molecules with accuracies better than 10%, even when using synthetic gradient retention data. Two distinct challenges in fitting gradient retention data were identified: 1) a lack of 'uniqueness' in the parameters; and 2) an inability to find the global optimum fit in a complex fitting landscape. Working with experimental data where measurement noise is unavoidable will only make the accuracy worse. This article is protected by copyright. All rights reserved.

Thermal modulation to enhance two-dimensional liquid chromatography separations of polymers

Many materials used in a wide range of fields consist of polymers that feature great structural complexity. One particularly suitable technique for characterising these complex polymers, that often feature correlated distributions in e.g. microstructure, chemical composition, or molecular weight, is comprehensive two-dimensional liquid chromatography (LC × LC). For example, using a combination of reversed-phase LC and size-exclusion chromatography (RPLC × SEC). Efficient and sensitive LC × LC often requires focusing of the analytes between the two stages. For the analysis of large-molecule analytes, such as synthetic polymers, thermal modulation (or cold trapping) may be feasible. This approach is studied for the analysis of a styrene/butadiene "star" block copolymer. Trapping efficiency is evaluated qualitatively by monitoring the effluent of the trap with an evaporative light-scattering detector and quantitatively by determining the recovery of polystyrene standards from RPLC × SEC experiments. The recovery was dependant on the molecular weight and the temperatures of the first-dimension column and of the trap, and ranged from 46% for a molecular weight of 2.78 kDa to 86% (or up to 94.5% using an optimized set-up) for a molecular weight of 29.15 kDa, all at a first-dimension-column temperature of 80 °C and a trap temperature of 5 °C. Additionally a strategy to reduce the pressure pulse from the modulation has been developed, bringing it down from several tens of bars to only a few bar.

Measuring and using scanning-gradient data for use in method optimization for liquid chromatography

The use of scanning gradients can significantly reduce method-development time in reversed-phase liquid chromatography. However, there is no consensus on how they can best be used. In the present work we set out to systematically investigate various factors and to formulate guidelines. Scanning gradients are used to establish retention models for individual analytes. Different retention models were compared by computing the Akaike information criterion and the prediction accuracy. The measurement uncertainty was found to influence the optimum choice of model. The use of a third parameter to account for non-linear relationships was consistently found not to be statistically significant. The duration (slope) of the scanning gradients was not found to influence the accuracy of prediction. The prediction error may be reduced by repeating scanning experiments or - preferably - by reducing the measurement uncertainty. It is commonly assumed that the gradient-slope factor, i.e. the ratio between slopes of the fastest and the slowest scanning gradients, should be at least three. However, in the present work we found this factor less important than the proximity of the slope of the predicted gradient to that of the scanning gradients. Also, interpolation to a slope between that of the fastest and the slowest scanning gradient is preferable to extrapolation. For comprehensive two-dimensional liquid chromatography (LC × LC) our results suggest that data obtained from fast second-dimension gradients cannot be used to predict retention in much slower first-dimension gradients.

Recent applications of retention modelling in liquid chromatography

Recent applications of retention modelling in liquid chromatography (2015–2020) are comprehensively reviewed. The fundamentals of the field, which date back much longer, are summarized. Retention modeling is used in retention‐mechanism studies, for determining physical parameters, such as lipophilicity, and for various more‐practical purposes, including method development and optimization, method transfer, and stationary‐phase characterization and comparison. The review focusses on the effects of mobile‐phase composition on retention, but other variables and novel models to describe their effects are also considered. The five most‐common models are addressed in detail, i.e. the log‐linear (linear‐solvent‐strength) model, the quadratic model, the log–log (adsorption) model, the mixed‐mode model, and the Neue–Kuss model. Isocratic and gradient‐elution methods are considered for determining model parameters and the evaluation and validation of fitted models is discussed. Strategies in which retention models are applied for developing and optimizing one‐ and two‐dimensional liquid chromatographic separations are discussed. The review culminates in some overall conclusions and several concrete recommendations.